Elementary equation

Dec 2015
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169
Earth
Given equation \(\displaystyle x=x^2 \) which has two real solutions 0 and 1.
Solve the equation using approximation (Newton’s method).
Can anyone post it in short-terms (also other approximations)?
 
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skipjack

Forum Staff
Dec 2006
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Newton-Raphson method: if $x$ is your first approximation (nearer to 0 or 1 than to 1/2), use $x^2/(2x - 1)$ as your next approximation.
 
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